solids have, in general, elasticity both as to change in volume and as to change in shape, a solid medium can transmit two kinds of waves. compressional and transverse. (See WAvEs.) A solid rod, too, can vibrate in several way.: longitudinally. if it is stroked length wise; torsionally. if it is twisted: from side to side, like a tuning-fork, if it is bent.
FLums. A fluid is defined to he such a form Of matter as will yield to a shearing force, how ever small. Thus it is necessary to discus: the elasticity of fluids with reference to changes in volume only. As before, the definition of the coefficient of elasticity is A)) Ar where r is the original volume, and AP is the decrease in the volume aceompanying an increase in the internal pressure of an amount Ap. For liquids • is very large. since they are so slightly compressible: for a gas. however, it is much smaller. When any portion of matter is com pressed. the temperature is increased (except in most special cases) ; and this fact alters the lalue of the change of pressure corresponding to a definite change in volume. Tf the change in xoltime is to he due to the change in pressure alone, it is necessary to change the volume so slow ly that the temperature remains practically eon .tant. This fact is of particular importance in the ease of ,uses, because they are so easily com pressed and there is accordingly such a great rise in temperature care is taken. If •the vol.. VI —47.
gas is compressed so suddenly that the whole change in volume takes place before there is tittle for any loss of heat by radiation or con duction, the temperature will rise greatly, and this will produ•e a marked increase in the prey sure of the gas. thus increasing the coefficient of
elasticity for the gas.
The coefficient for a gas, hen tImre is no change in temperature, lusty be calculated from Boyle's law for a gas, which states that, as long as the temperature of a gas does not change, the product of its pressure and volume remains con stant, however the volume is altered. Thus, if • is the volume of the gas when the pressure is p, and r —At., the volume when the pressure is increased to p .gyp, then Pr = (p r — = p'--p A ± if 'p and Ar are so small that their product may be neglected. Bence pA r = r Ap and therefore In words, the coefficient of elasticity for a gas at constant temperature numerically equals its pressure. lf, however, the change ill volume is made so rapidly that the heat produced has no time to escape. the coefficient equals ;T. where y is a constant for any one gas, being equal to the ratio of the specific heat at constant pressure to that at constant volume. (See PEAT.) For air, hydro gen. and oxygen ), very nearly equals Li.
A. fluid medium can transmit compressional waves only: and in these the vibrations must be rapid. otherwise the fluid would flow round the vibrating body which is the cause of the waves. Therefore, the elasticity which is called into play is the one corresponding, to no escape of heat.